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It is not safe nor do you want to reuse something that is full of the juices that your meat leached out during the brine or marinade. Also, If you are going to use your marinade as a basting sauce you need to set some aside prior to marinating the meat to keep the basting sauce safe.
It depends. I will when doing my wings on the fire pit and skewers.
You can bring the marinade to a simmer for a bit and it should be fine to use while cooking.
I'll shoot some pics tomorrow.
If I were to marinate then remove the product from the marinade for later use to use as a sauce, I would simmer it before placing in the refrigerator, I have done this before with no problem and feel it's perfectly safe if you simmer the marinade for a bit, provided the marinade was handled properly from the beginning.